Asymptotic Properties of Nonlinear Least Squares Estimates in Stochastic Regression Models

Abstract

Stochastic regression models of the form yi = fi(e)+EL, where the random increasing sequence of u-fields {Si) and fi is a random Si - l-measurable function of an unknown parameter 8, cover a broad range of nonlinear (and linear) time series and stochastic process models. Herein strong con- sistency and asymptotic normality of the least squares estimate of e in these stochastic regression models are established. In the linear case h(e) = eT$Ji, they reduce to known results on the linear least squares estimate (c;'$J~$JT)-~c;'$J~ disturbances EL form a martingale difference sequence with respect to an yi with stochastic GL- l-measurable regressors $Ji.